{"as_of":"2026-08-21T14:18:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:9137a284553c36e77bff45ceb2231aef7119863ce11397f204c1539edad4321f","coverage":[{"denominator":23,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":23,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-06T19:31:46.368142Z","state":"measured"},{"denominator":26,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":26,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-21T06:32:19.484+00:00","state":"measured"},{"denominator":3,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":3,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-01T07:13:05.155348Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"arxiv_reference","source_observed_at":"2026-07-03T01:17:30.674714Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2507.06115","last_updated":"2025-07-08T15:58:18Z","snapshot_observed_at":"2026-08-06T19:08:22.043305Z","submitted_at":"2025-07-08T15:58:18Z","title":"Optimal Young's convolutions inequality and its reverse form on the hypercube","version":1},"cited_work":{"arxiv_id":"2507.06115","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2507.06115","snapshot_observed_at":"2026-07-03T01:17:30.674714Z","title":"Optimal Young’s convolu- tions inequality and its reverse form on the hypercube.arXiv preprint arXiv:2507.06115, 2025","venue":null,"work_id":"0a124647-afcd-485d-b4de-0699420a6f0e","year":2025},"citing_paper":{"arxiv_id":"2606.08958","last_updated":"2026-06-08T03:00:40Z","snapshot_observed_at":"2026-07-06T23:48:21.633158Z","submitted_at":"2026-06-08T03:00:40Z","title":"A spectral correlation inequality for increasing Boolean functions","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-06-27T16:43:04.921041Z"},"links":{"cited_paper":"/paper/2507.06115","citing_paper":"/paper/2606.08958"},"observation_digest":"sha256:d7a4ca2d197dc867c91b8e3196235145edd01b9945bf6f786cb008473790b06e","observation_id":"0884e1a3-b3cd-47f8-8852-bb4c30eb8ace","resolution":{"observed_at":"2026-07-03T01:17:30.676627Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2507.06115","last_updated":"2025-07-08T15:58:18Z","snapshot_observed_at":"2026-08-06T19:08:22.043305Z","submitted_at":"2025-07-08T15:58:18Z","title":"Optimal Young's convolutions inequality and its reverse form on the hypercube","version":1},"cited_work":{"arxiv_id":"2507.06115","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2507.06115","snapshot_observed_at":"2026-07-03T01:17:30.674714Z","title":"Optimal Young’s convolu- tions inequality and its reverse form on the hypercube.arXiv preprint arXiv:2507.06115, 2025","venue":null,"work_id":"0a124647-afcd-485d-b4de-0699420a6f0e","year":2025},"citing_paper":{"arxiv_id":"2606.32024","last_updated":"2026-06-30T17:52:59Z","snapshot_observed_at":"2026-07-07T00:05:41.920778Z","submitted_at":"2026-06-30T17:52:59Z","title":"The sharp diagonal spectral correlation inequality on the discrete cube","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-07-01T04:17:25.416483Z"},"links":{"cited_paper":"/paper/2507.06115","citing_paper":"/paper/2606.32024"},"observation_digest":"sha256:e399a82413b634a6f3293106e9dc000b2a2c78a86ecfcaf6b006769c4f0ca945","observation_id":"ce666652-1f55-4a4a-8413-db56bb887e0d","resolution":{"observed_at":"2026-07-01T11:35:43.237911Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2507.06115","last_updated":"2025-07-08T15:58:18Z","snapshot_observed_at":"2026-08-06T19:08:22.043305Z","submitted_at":"2025-07-08T15:58:18Z","title":"Optimal Young's convolutions inequality and its reverse form on the hypercube","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2507.06115","snapshot_observed_at":"2026-08-01T07:13:05.155348Z","title":"Beltran, P","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.21589","last_updated":"2026-07-23T17:58:16Z","snapshot_observed_at":"2026-08-17T03:01:59.762071Z","submitted_at":"2026-07-23T17:58:16Z","title":"The Frankl--Tokushige product conjectures for $r$-cross-intersecting families","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-01T07:13:05.155348Z"},"links":{"cited_paper":"/paper/2507.06115","citing_paper":"/paper/2607.21589"},"observation_digest":"sha256:fe2fb3a8a054dcdab94e336c1f454c9a485ae188b0a5a126858f6f882265e6bf","observation_id":"9b5fddbd-9256-4e4b-aefb-37a9dd84eee2","resolution":{"observed_at":"2026-08-01T07:13:05.155348Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2507.06115/citation-record","integrity":"/paper/2507.06115/integrity","json":"/paper/2507.06115/citation-record.json","paper":"/paper/2507.06115"},"outbound":[{"citation":{"cited_paper":{"arxiv_id":"2404.04486","last_updated":"2024-04-15T15:25:18Z","snapshot_observed_at":"2026-08-16T14:03:12.201955Z","submitted_at":"2024-04-06T03:40:13Z","title":"Discrete Brunn-Minkowski Inequality for subsets of the cube","version":2},"cited_work":{"arxiv_id":"2404.04486","doi":null,"metadata_source":"pith","pith_arxiv_id":"2404.04486","snapshot_observed_at":"2026-08-06T19:31:46.498752Z","title":"Discrete Brunn-Minkowski Inequality for subsets of the cube","venue":"math.CO","work_id":"83f9e32f-a29a-440d-92ee-b31038303771","year":2024},"citing_paper":{"arxiv_id":"2507.06115","last_updated":"2025-07-08T15:58:18Z","snapshot_observed_at":"2026-08-06T19:08:22.043305Z","submitted_at":"2025-07-08T15:58:18Z","title":"Optimal Young's convolutions inequality and its reverse form on the hypercube","version":1},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-08-06T19:31:46.263795Z"},"links":{"cited_paper":"/paper/2404.04486","citing_paper":"/paper/2507.06115"},"observation_digest":"sha256:4dc6759ad17d5c7a5329b643aab0b2ba7b4102aa7fac5972f3e5540104317516","observation_id":"a58e331b-970f-4d7c-b646-085ff4969a61","resolution":{"observed_at":"2026-08-06T19:31:46.503628Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2409.12579","last_updated":"2024-10-14T17:16:28Z","snapshot_observed_at":"2026-08-16T13:17:14.947184Z","submitted_at":"2024-09-19T09:00:20Z","title":"Sharp estimates for Gowers norms on discrete cubes","version":2},"cited_work":{"arxiv_id":"2409.12579","doi":null,"metadata_source":"pith","pith_arxiv_id":"2409.12579","snapshot_observed_at":"2026-08-06T19:31:46.473317Z","title":"Sharp estimates for Gowers norms on discrete cubes","venue":"math.CO","work_id":"1b105473-b19b-484f-97e2-c08c12a4ccd5","year":2024},"citing_paper":{"arxiv_id":"2507.06115","last_updated":"2025-07-08T15:58:18Z","snapshot_observed_at":"2026-08-06T19:08:22.043305Z","submitted_at":"2025-07-08T15:58:18Z","title":"Optimal Young's convolutions inequality and its reverse form on the hypercube","version":1},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-08-06T19:31:46.269648Z"},"links":{"cited_paper":"/paper/2409.12579","citing_paper":"/paper/2507.06115"},"observation_digest":"sha256:8021f7c04210e3c23a471be443709e63c6e7af8dc86b0e258a6172109ec67891","observation_id":"484dc26e-bbd4-4880-9bc8-394d0fb5cd76","resolution":{"observed_at":"2026-08-06T19:31:46.479466Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:31:46.817647Z","title":"Explicit constructions of RIP matrices and related problems","venue":null,"work_id":"36c21005-b005-4fec-ac68-8dbec8cc9efc","year":2011},"citing_paper":{"arxiv_id":"2507.06115","last_updated":"2025-07-08T15:58:18Z","snapshot_observed_at":"2026-08-06T19:08:22.043305Z","submitted_at":"2025-07-08T15:58:18Z","title":"Optimal Young's convolutions inequality and its reverse form on the hypercube","version":1},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-08-06T19:31:46.274826Z"},"links":{"citing_paper":"/paper/2507.06115"},"observation_digest":"sha256:4c9190961682a6c6f1be47fa727dbd0f33c3c1c66c6461874838cb988c6eab2c","observation_id":"bd166f4f-f63b-42f5-8ef0-2693c01caa6c","resolution":{"observed_at":"2026-08-06T19:31:46.822984Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2507.01359","last_updated":"2025-07-02T04:50:11Z","snapshot_observed_at":"2026-08-12T04:50:26.134069Z","submitted_at":"2025-07-02T04:50:11Z","title":"Inequalities in Fourier analysis on binary cubes","version":1},"cited_work":{"arxiv_id":"2507.01359","doi":null,"metadata_source":"pith","pith_arxiv_id":"2507.01359","snapshot_observed_at":"2026-08-06T19:31:46.449516Z","title":"Inequalities in Fourier analysis on binary cubes","venue":"math.CA","work_id":"1993f847-b548-4eb0-9ad1-bc263d4d92e4","year":2025},"citing_paper":{"arxiv_id":"2507.06115","last_updated":"2025-07-08T15:58:18Z","snapshot_observed_at":"2026-08-06T19:08:22.043305Z","submitted_at":"2025-07-08T15:58:18Z","title":"Optimal Young's convolutions inequality and its reverse form on the hypercube","version":1},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-08-06T19:31:46.279752Z"},"links":{"cited_paper":"/paper/2507.01359","citing_paper":"/paper/2507.06115"},"observation_digest":"sha256:64e97ca50131cdec738547136c288f63afae3756e6407579804d2e3ff9864163","observation_id":"932a9aac-e6bc-4876-a7b8-c8f9bef0dc17","resolution":{"observed_at":"2026-08-06T19:31:46.455281Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:31:46.798535Z","title":"Additive energies on discrete cubes","venue":null,"work_id":"a3ef8bd3-c3f0-4d2a-a9fe-95a390ee784e","year":2023},"citing_paper":{"arxiv_id":"2507.06115","last_updated":"2025-07-08T15:58:18Z","snapshot_observed_at":"2026-08-06T19:08:22.043305Z","submitted_at":"2025-07-08T15:58:18Z","title":"Optimal Young's convolutions inequality and its reverse form on the hypercube","version":1},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-08-06T19:31:46.284866Z"},"links":{"citing_paper":"/paper/2507.06115"},"observation_digest":"sha256:87eacddd21b5d4373c83c623f9e74afd78fc68b55aa4a45ef65dc9803daf5a8c","observation_id":"675f3302-1994-47e4-b0eb-b7b6e545a14a","resolution":{"observed_at":"2026-08-06T19:31:46.803997Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:31:46.781883Z","title":"Hajela and P","venue":null,"work_id":"a7fb1e85-462c-4b38-800f-712aeaa119d2","year":1985},"citing_paper":{"arxiv_id":"2507.06115","last_updated":"2025-07-08T15:58:18Z","snapshot_observed_at":"2026-08-06T19:08:22.043305Z","submitted_at":"2025-07-08T15:58:18Z","title":"Optimal Young's convolutions inequality and its reverse form on the hypercube","version":1},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-08-06T19:31:46.289548Z"},"links":{"citing_paper":"/paper/2507.06115"},"observation_digest":"sha256:c0191a4ae2a2860c0cd95ef9a09a1b30086f74f814be6e75934a8002d147da66","observation_id":"27a0c509-41d0-4f0c-8471-5baecc7548e6","resolution":{"observed_at":"2026-08-06T19:31:46.786814Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:31:46.764053Z","title":"A bound on partitioning clusters","venue":null,"work_id":"5cffb0ef-3a05-41cb-9fe4-8ebe31447428","year":2017},"citing_paper":{"arxiv_id":"2507.06115","last_updated":"2025-07-08T15:58:18Z","snapshot_observed_at":"2026-08-06T19:08:22.043305Z","submitted_at":"2025-07-08T15:58:18Z","title":"Optimal Young's convolutions inequality and its reverse form on the hypercube","version":1},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-08-06T19:31:46.294862Z"},"links":{"citing_paper":"/paper/2507.06115"},"observation_digest":"sha256:0d65e99cbb98ab740dc9e755ed89441bb0f711d5fd147905c6d0064965b6c4c5","observation_id":"9bfa05b6-5590-4dcb-8620-7c498439ab76","resolution":{"observed_at":"2026-08-06T19:31:46.769478Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:31:46.747037Z","title":"Leindler","venue":null,"work_id":"05ba2dc9-49f8-463b-aa79-0dcd6531c6f9","year":1971},"citing_paper":{"arxiv_id":"2507.06115","last_updated":"2025-07-08T15:58:18Z","snapshot_observed_at":"2026-08-06T19:08:22.043305Z","submitted_at":"2025-07-08T15:58:18Z","title":"Optimal Young's convolutions inequality and its reverse form on the hypercube","version":1},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-08-06T19:31:46.299383Z"},"links":{"citing_paper":"/paper/2507.06115"},"observation_digest":"sha256:d5de537c6184bfc0393a517755aea32db78e66c1eaa71245d2f82f49fb26087f","observation_id":"d9691a60-0097-4699-99d8-4b7aeac400ec","resolution":{"observed_at":"2026-08-06T19:31:46.752136Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:31:46.729623Z","title":"Shkredov","venue":null,"work_id":"84878792-f0ce-4421-86d8-45f67a848f5e","year":2013},"citing_paper":{"arxiv_id":"2507.06115","last_updated":"2025-07-08T15:58:18Z","snapshot_observed_at":"2026-08-06T19:08:22.043305Z","submitted_at":"2025-07-08T15:58:18Z","title":"Optimal Young's convolutions inequality and its reverse form on the hypercube","version":1},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-08-06T19:31:46.304012Z"},"links":{"citing_paper":"/paper/2507.06115"},"observation_digest":"sha256:17adc9ba544e392ead12365f01e424dc3c5a70aef3f0bf3cf78407f75b279ba1","observation_id":"2971ce90-f33d-4230-8b2b-b056c8f180a5","resolution":{"observed_at":"2026-08-06T19:31:46.734663Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:31:46.709921Z","title":"Energies and structure of additive sets","venue":null,"work_id":"34e1e785-7044-4f3c-ac79-743fd305fb6b","year":2014},"citing_paper":{"arxiv_id":"2507.06115","last_updated":"2025-07-08T15:58:18Z","snapshot_observed_at":"2026-08-06T19:08:22.043305Z","submitted_at":"2025-07-08T15:58:18Z","title":"Optimal Young's convolutions inequality and its reverse form on the hypercube","version":1},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-08-06T19:31:46.308944Z"},"links":{"citing_paper":"/paper/2507.06115"},"observation_digest":"sha256:3bd68f8257fcaabd3bd4eb800b87c8c7d225f625b575989bdf301cb9b0dab15d","observation_id":"495c1408-b199-4521-bb47-8559e66d8030","resolution":{"observed_at":"2026-08-06T19:31:46.714970Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:31:46.690912Z","title":null,"venue":null,"work_id":"0a4a497d-b311-46ce-93d6-ae5c51a72ded","year":1977},"citing_paper":{"arxiv_id":"2507.06115","last_updated":"2025-07-08T15:58:18Z","snapshot_observed_at":"2026-08-06T19:08:22.043305Z","submitted_at":"2025-07-08T15:58:18Z","title":"Optimal Young's convolutions inequality and its reverse form on the hypercube","version":1},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-08-06T19:31:46.313403Z"},"links":{"citing_paper":"/paper/2507.06115"},"observation_digest":"sha256:6cb6080bab5755e25e9279a63448518d1c01be965c692fc19ba063bb02977625","observation_id":"e4fa8083-ec56-493c-ae39-9a81c2b1497e","resolution":{"observed_at":"2026-08-06T19:31:46.697682Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:31:46.665710Z","title":"Bourgain, S","venue":null,"work_id":"7b90cc4d-486e-43a7-ac83-205ee5f0db0f","year":2011},"citing_paper":{"arxiv_id":"2507.06115","last_updated":"2025-07-08T15:58:18Z","snapshot_observed_at":"2026-08-06T19:08:22.043305Z","submitted_at":"2025-07-08T15:58:18Z","title":"Optimal Young's convolutions inequality and its reverse form on the hypercube","version":1},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-08-06T19:31:46.318243Z"},"links":{"citing_paper":"/paper/2507.06115"},"observation_digest":"sha256:785f40d6a85fb0ab2c71db76702fb440af62da5aa29a2a0ccf4cc48a9362e56c","observation_id":"56ad6965-e613-44c9-ab67-f4af049682fb","resolution":{"observed_at":"2026-08-06T19:31:46.671290Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:31:46.647310Z","title":"de Dios, R","venue":null,"work_id":"4fc689ec-fca4-44c5-add7-16558190fa62","year":null},"citing_paper":{"arxiv_id":"2507.06115","last_updated":"2025-07-08T15:58:18Z","snapshot_observed_at":"2026-08-06T19:08:22.043305Z","submitted_at":"2025-07-08T15:58:18Z","title":"Optimal Young's convolutions inequality and its reverse form on the hypercube","version":1},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-08-06T19:31:46.322745Z"},"links":{"citing_paper":"/paper/2507.06115"},"observation_digest":"sha256:78d3367190c7d90bb17b4b8e46cc2cb3285529f4ba2cb73058f1fa525350d229","observation_id":"0a1615af-38d7-4efc-8f0e-909bffc54dc7","resolution":{"observed_at":"2026-08-06T19:31:46.652795Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:31:46.629708Z","title":"Fish, Ben Lund, and A","venue":null,"work_id":"1814bbf7-3d24-4ca6-bc3f-108f0a0ee6ae","year":2019},"citing_paper":{"arxiv_id":"2507.06115","last_updated":"2025-07-08T15:58:18Z","snapshot_observed_at":"2026-08-06T19:08:22.043305Z","submitted_at":"2025-07-08T15:58:18Z","title":"Optimal Young's convolutions inequality and its reverse form on the hypercube","version":1},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-08-06T19:31:46.327248Z"},"links":{"citing_paper":"/paper/2507.06115"},"observation_digest":"sha256:2b8796fa3f70e97bcc59ee5b520d7baba6f175802180ac434f25e318854bbc94","observation_id":"0d3c1ff1-a89b-4957-ab3a-62ce6aa0d89e","resolution":{"observed_at":"2026-08-06T19:31:46.633967Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:31:46.613464Z","title":"Gyarmati, M","venue":null,"work_id":"ad972b24-57d4-4f23-ab7a-e6457cdaa090","year":null},"citing_paper":{"arxiv_id":"2507.06115","last_updated":"2025-07-08T15:58:18Z","snapshot_observed_at":"2026-08-06T19:08:22.043305Z","submitted_at":"2025-07-08T15:58:18Z","title":"Optimal Young's convolutions inequality and its reverse form on the hypercube","version":1},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-08-06T19:31:46.331630Z"},"links":{"citing_paper":"/paper/2507.06115"},"observation_digest":"sha256:4a36110b2769d84d001b5bc9c6f3cb0ec57b9317dad9a598a7786cdb882c2dee","observation_id":"2f5696d8-27b6-461d-8e95-9d5603c49f34","resolution":{"observed_at":"2026-08-06T19:31:46.618570Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:31:46.596470Z","title":"Green, D","venue":null,"work_id":"c4aed0cb-3a08-4207-9546-d2fbe0ca785e","year":null},"citing_paper":{"arxiv_id":"2507.06115","last_updated":"2025-07-08T15:58:18Z","snapshot_observed_at":"2026-08-06T19:08:22.043305Z","submitted_at":"2025-07-08T15:58:18Z","title":"Optimal Young's convolutions inequality and its reverse form on the hypercube","version":1},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-08-06T19:31:46.336027Z"},"links":{"citing_paper":"/paper/2507.06115"},"observation_digest":"sha256:6b9787e13dc983348d76bd9b014f6f44c6bd0d306d0f25cabe7c9e8b24a7b359","observation_id":"664f63bb-7185-4ad2-9131-8ad5005a1773","resolution":{"observed_at":"2026-08-06T19:31:46.601844Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:31:46.579951Z","title":null,"venue":null,"work_id":"cade985d-1dbd-4cf3-8b0d-f3a5995dc00d","year":2006},"citing_paper":{"arxiv_id":"2507.06115","last_updated":"2025-07-08T15:58:18Z","snapshot_observed_at":"2026-08-06T19:08:22.043305Z","submitted_at":"2025-07-08T15:58:18Z","title":"Optimal Young's convolutions inequality and its reverse form on the hypercube","version":1},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-08-06T19:31:46.341217Z"},"links":{"citing_paper":"/paper/2507.06115"},"observation_digest":"sha256:b75dbc22084c4a44b4f42ad1de4561cea3415fac3fd46e2af50c35cab5ba8c8a","observation_id":"ce437220-8057-430d-8366-1b7ba1f85aa9","resolution":{"observed_at":"2026-08-06T19:31:46.584614Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:31:46.564205Z","title":"Hanson and G","venue":null,"work_id":"91820177-8df0-448a-a907-925d31031d3e","year":2021},"citing_paper":{"arxiv_id":"2507.06115","last_updated":"2025-07-08T15:58:18Z","snapshot_observed_at":"2026-08-06T19:08:22.043305Z","submitted_at":"2025-07-08T15:58:18Z","title":"Optimal Young's convolutions inequality and its reverse form on the hypercube","version":1},"reference_index":18,"source":"arxiv_source","source_observed_at":"2026-08-06T19:31:46.346065Z"},"links":{"citing_paper":"/paper/2507.06115"},"observation_digest":"sha256:e14f1d65ee86a15ab154753f556c943ed4a478000c0b6bb2e8e83eaa8d07a2e4","observation_id":"3c712501-bbdd-4038-8436-0e2a866ae0be","resolution":{"observed_at":"2026-08-06T19:31:46.568754Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:31:46.548412Z","title":"Ivanisvili, Convolution estimates and the number of disjoint partitions, The Electronic Journal of Combinatorics, Volume 24, Issue 2 (2017), Paper P2.43","venue":null,"work_id":"ff0942bf-f4de-4a0e-8c91-3d29b849412a","year":2017},"citing_paper":{"arxiv_id":"2507.06115","last_updated":"2025-07-08T15:58:18Z","snapshot_observed_at":"2026-08-06T19:08:22.043305Z","submitted_at":"2025-07-08T15:58:18Z","title":"Optimal Young's convolutions inequality and its reverse form on the hypercube","version":1},"reference_index":19,"source":"arxiv_source","source_observed_at":"2026-08-06T19:31:46.350482Z"},"links":{"citing_paper":"/paper/2507.06115"},"observation_digest":"sha256:6c5dc3e094fa3e132a39f68452aeb24cb034d26f5fb8a5085559b49b2f3732f4","observation_id":"d9cbea1d-2730-48a7-a48b-a7343063bbe6","resolution":{"observed_at":"2026-08-06T19:31:46.553182Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2206.01591","last_updated":"2023-06-05T21:40:17Z","snapshot_observed_at":"2026-08-16T16:55:29.999439Z","submitted_at":"2022-06-03T14:21:21Z","title":"On binomial sums, additive energies, and lazy random walks","version":5},"cited_work":{"arxiv_id":"2206.01591","doi":null,"metadata_source":"pith","pith_arxiv_id":"2206.01591","snapshot_observed_at":"2026-08-06T19:31:46.425100Z","title":"On binomial sums, additive energies, and lazy random walks","venue":"math.CA","work_id":"bec2ccfa-ccab-42d0-bbb8-52afde1503ee","year":2022},"citing_paper":{"arxiv_id":"2507.06115","last_updated":"2025-07-08T15:58:18Z","snapshot_observed_at":"2026-08-06T19:08:22.043305Z","submitted_at":"2025-07-08T15:58:18Z","title":"Optimal Young's convolutions inequality and its reverse form on the hypercube","version":1},"reference_index":20,"source":"arxiv_source","source_observed_at":"2026-08-06T19:31:46.354760Z"},"links":{"cited_paper":"/paper/2206.01591","citing_paper":"/paper/2507.06115"},"observation_digest":"sha256:4353f7daf3ca7a5fb2b0254a9ea7923a9cddcf93286bacb85bc5305ad1e708c0","observation_id":"35d40614-5fd1-48be-b5f1-e8bc250144f4","resolution":{"observed_at":"2026-08-06T19:31:46.431443Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:31:46.533074Z","title":"Kane and T","venue":null,"work_id":"426ee022-9ab5-45e7-b4d0-403973cf53bd","year":2017},"citing_paper":{"arxiv_id":"2507.06115","last_updated":"2025-07-08T15:58:18Z","snapshot_observed_at":"2026-08-06T19:08:22.043305Z","submitted_at":"2025-07-08T15:58:18Z","title":"Optimal Young's convolutions inequality and its reverse form on the hypercube","version":1},"reference_index":21,"source":"arxiv_source","source_observed_at":"2026-08-06T19:31:46.359486Z"},"links":{"citing_paper":"/paper/2507.06115"},"observation_digest":"sha256:768330e92b691c9bfed98f130e247d7e317887cf0201483a10c6d9f35d1e446f","observation_id":"27c2f468-0fcf-4ced-92c9-993d5a0f2aed","resolution":{"observed_at":"2026-08-06T19:31:46.537984Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s00493-021-4547-0","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T00:03:40.895421Z","title":"Matolcsi, I","venue":"COMBINATORICA","work_id":"a4dd2d31-cd08-43b0-8539-77fea704fc01","year":2022},"citing_paper":{"arxiv_id":"2507.06115","last_updated":"2025-07-08T15:58:18Z","snapshot_observed_at":"2026-08-06T19:08:22.043305Z","submitted_at":"2025-07-08T15:58:18Z","title":"Optimal Young's convolutions inequality and its reverse form on the hypercube","version":1},"reference_index":22,"source":"arxiv_source","source_observed_at":"2026-08-06T19:31:46.363775Z"},"links":{"citing_paper":"/paper/2507.06115"},"observation_digest":"sha256:5aa712ad39a371d0c9203ceb13c1ccf256c517981f3bcd3c9c2664422a5f9ff0","observation_id":"063f5ad5-c962-4e7f-87b1-d21bc206fb6f","resolution":{"observed_at":"2026-08-06T19:31:46.406050Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:31:46.515697Z","title":null,"venue":null,"work_id":"8d7956b3-70e0-40bf-b2fa-6ce4bfb93f95","year":2006},"citing_paper":{"arxiv_id":"2507.06115","last_updated":"2025-07-08T15:58:18Z","snapshot_observed_at":"2026-08-06T19:08:22.043305Z","submitted_at":"2025-07-08T15:58:18Z","title":"Optimal Young's convolutions inequality and its reverse form on the hypercube","version":1},"reference_index":23,"source":"arxiv_source","source_observed_at":"2026-08-06T19:31:46.368142Z"},"links":{"citing_paper":"/paper/2507.06115"},"observation_digest":"sha256:c8c76003b84a783a4cc0143108ebb628dad98847dc10c3bd159f0230067e1b1f","observation_id":"6f5a5950-8000-497b-9555-311295133225","resolution":{"observed_at":"2026-08-06T19:31:46.521507Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2507.06115","last_updated":"2025-07-08T15:58:18Z","latest_version":1,"primary_category":"math.CA","snapshot_observed_at":"2026-08-06T19:08:22.043305Z","submitted_at":"2025-07-08T15:58:18Z","title":"Optimal Young's convolutions inequality and its reverse form on the hypercube"},"reference_resolution":{"displayed":23,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":3,"verified_exact":5,"verified_fuzzy":15},"total_outbound_references":23},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"thesis":"As of 21 August 2026, this Paper Citation Record lists 23 of 23 outbound references and 3 inbound Pith citation observations for arXiv:2507.06115."}